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collinear wanted, incenter, circumcircle, angle bisectors related

Source: 2015 Saudi Arabia Pre-TST 3.1

September 12, 2020
geometryincentercircumcircleangle bisectorcollinear

Problem Statement

Let ABCABC be a triangle, II its incenter, and DD a point on the arc BCBC of the circumcircle of ABCABC not containing AA. The bisector of the angle ∠ADB\angle ADB intesects the segment ABAB at EE. The bisector of the angle ∠CDA\angle CDA intesects the segment ACAC at FF. Prove that the points E,F,IE, F,I are collinear.
(Malik Talbi)
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